But it’s also about the tenacity of the survivors. The probability that people are enjoying Beyoncé in 2113, in a hundred years, is 1% — not too bad odds.

(It becomes even more entertaining to think about when one learns that it’s not just social survival but also daily rainfall and city populations and personal wealth are also apparently Pareto-distributed. If it’s rained 10 inches already today, there’s a 1% probability that it’ll have rained 100 inches by midnight!)

So I wonder if, while the expected value of X | X>k is 2*k, the full density was flat-ish between k+1 to 2*k? or at least interesting enough to shed some light on why the expectation is the worst predictor just before the extinction. Thanks! I’ll try to make Wolfram Alpha show me the answer in the meantime.

If you find a distribution that fits your data, then you can compute the distribution on continued loyalty conditional on loyalty to date. If your data follow a power law, you get a simple distribution, the Lindy effect. But in general you’ll get something else, similar to the Lindy effect if your distribution is similar to a power law.

Thanks,
Jamil

One thing I’ve noticed here is that, when looking at other math problems, the devils is in the definition. When talking about whether a programming language “will be around” in a given period of time, we should really ask what this means. I’m sure that in 25 years, you’ll be able to find a program written somewhere in Perl that is still in use and being maintained. Even if there’s only one such application, does that mean Perl is “in use”? Then there’s situations like JavaScript, where a whole bunch of languages and tools essential boil down to writing JS without actually writing JS. Does that mean it’s “in use”, even if almost no one actually writes JS code directly?

It’s the same with popular music. Look hard enough, and you’ll find someone who is a fan of any given song or artist. Are they still considered popular? What if there’s a one-off tribute festival for some obscure artist one year, with thousands of attendees?

I do agree the statement is a probabilistic statement and not a law. It should also be subject to clearly defined terms, but on the whole, it’s a good guide.

“… So we might expect Beyoncé to fade into obscurity no sooner than a decade from now, the Beatles no sooner than four decades from now, and Beethoven no sooner than a couple centuries from now… ”

Seems like the effect suggests that things will last at least as long as they have, not that they will only last as long as they have?

As for Beyoncé versus a large ensemble of Beyoncés, that’s what probability means (at least the frequentist interpretation of probability). Or from a more Bayesian perspective, it’s a statement not about Beyoncé per se but our uncertain knowledge of her future career, informed by the careers of other artists.

Derek: The example of Bach’s career is interesting, and the Lindy effect is too simple to take such things into account.

I was thinking about Windows in light of the Lindy effect. When did Windows begin? Do you go back to DOS in 1981, or Windows 1.0 in 1985? I’d say there was a pretty sharp discontinuity in its history in 1993 with Windows NT and that current versions of Windows are descendents of NT, not really Windows 1.0 or DOS. Linux, on the other hand, seems like more of a direct descendent of the original Unix versions.

Human life expectancy follows a double exponential law.

Software system lifetime seems to have an exponential distribution (fig 3 of the link).

What process would generate power law lifetimes? If available resources were governed by a fractal process and different entities consumed different ‘size’ objects we would expect lifetime to follow a power law.

Some kind of variation on the game of life where memory was divided into chunks and activity stopped once all the chunks were used up?

Also, even if musician legacy lifetimes were to obey a power law, it still doesn’t tell us what to expect about Beyoncé, but only about the statistics of a pretty large ensemble of Beyoncés (perish the thought!)